Project ForgeEngineering Mathematics
Calculus
GATE 2020
Hard
Let I = ∫(x=0 to 1) ∫(y=0 to x²) xy² dy dx. Then, I may also be expressed as
- A∫(y=0 to 1) ∫(x=0 to √y) xy² dx dy
- B∫(y=0 to 1) ∫(x=√y to 1) yx² dx dy
- ∫(y=0 to 1) ∫(x=√y to 1) xy² dx dy
- D∫(y=0 to 1) ∫(x=0 to √y) yx² dx dy
Explanation
The original region is 0≤x≤1, 0≤y≤x². Reversing the order: for a given y (0≤y≤1), since y≤x² means x≥√y, and x≤1, x ranges from √y to 1. So I = ∫(y=0 to 1)∫(x=√y to 1) xy² dx dy — option (C).
Source: GATE ME 2020 Session 2 (ME-2) (2020)
This question is part of a 15-day revision cycle — sign in and Project Forge will bring it back the day before you'd forget it.